Quote:
Originally Posted by John May
... remove a battery and put it in voltmetr, it shows 4,2V, so I think battery is ok. ...
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Faulty logic!
Even a nearly dead battery will yield nearly its full voltage when there is no load. I modern voltmeter places almost no load on the circuit it's testing. The better the meter the less the load. Even under load the battery used by the Kindle will produce nearly full voltage up until very near the end of its charge.
Testing with a volt meter is all but useless. It can't determine if a battery is failing or not.
The symptoms you list are the result of either a failing battery or a faulty charger/cable. If the Kindle with charge "completely" (green charge light) then the charger is OK and short runtime indicates a bad battery. Also, not being able to achieve a full charge may still be the fault of the battery.
Take HarryT's advice and contact Amazon.